Question

Perform the indicated operation using the two nonlinear functions shown below.

Answer 1

Answer: h(g(h(3))) = -2

Find:

$h(g(h(3)))$

First, we will find the value of h(3). Based on the graph, if x=3, h(x) = -1:

We now have:

$\begin{gathered} h(g(h(3))) \\ \Rightarrow h(g(-1)) \end{gathered}$

Now, we need to find g(-1). Looking at the table, we see that g(-1) = 0:

We now have:

$\begin{gathered} h(g(-1)) \\ \Rightarrow h(0) \end{gathered}$

We then need to look at the graph again to find h(0):

With this, we know that:

$\begin{gathered} h(g(h(3))) \\ \Rightarrow h(g(-1)) \\ \Rightarrow h(0)=-2 \end{gathered}$

Therefore, h(g(h(3))) = -2